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Aerodynamic Coefficient
History Aerodynamic Coefficients were first defined and used by Otto Lilienthal in the late 1800’s. He was a German aviation pioneer that obtained measurements on a cambered airfoil and published them in his book Birdflight as the Basis of Aviation (Anderson 76). In his book he described the normal and axial (“tangential”) forces by N = 0.13ηFV2 and T = 0.13θFV2 where F was the planform area of the wing in m2, V the freestream velocity in m/s, and N and T are units of kilogram force, and η and θ are the aerodynamic coefficients (Anderson 76). Over a period of thirty years the expressions for the aerodynamic coefficients changed into what we now use to describe the forces of Lift and Drag. L = q∞SCL D = q∞SCD Aerodynamic Coefficients in General Aerodynamic Coefficients are non-dimensional numbers that are used to determine the aerodynamic characteristics of an aircraft. They bring all planes into the same arena by having a ratio of forces rather than simply using the forces. So a large plane might have more lift than a small plane but have a smaller lift coefficient. Using the aerodynamic coefficients, efficiencies can quickly be compared. Aerodynamic Coefficients can be defined on an infinite wing, finite wing, or a whole aircraft. For an infinite wing, the coefficients are described with a lower case letter such as Cl. A finite wing produces wing-tip vortices which lower the lift coefficient and is described by CL. The whole aircraft can also be described by CL. The Aerodynamic Coefficients are primarily a function of the two aerodynamic angles (Alpha and Beta), as well as Mach and Reynolds numbers. Control surfaces deflections and propulsion systems can also change the coefficients. So, the aerodynamic coefficient can be written as C( ) = C( ) ( α,β,M,h,δs,Tc ) where α is the angle of attack, β is the sideslip angle, M is the Mach number, h is the altitude, δs is the surface deflection, and Tc is the thrust coefficient (Stevens and Lewis 75). Common Aerodynamic Coefficients for an aircraft Formulation of Aerodynamic Coefficients The Aerodynamic Coefficients above are all static and can be found by taking a stationary model in a wind tunnel and measuring the aerodynamic forces and moments. Once these are obtained, then the Aerodynamic Coefficients can be calculated with the above formulas. There is an advantage using the aerodynamic coefficients rather than the actual forces. Through dimensional analysis, the aerodynamic coefficients can be reduced to functions that depend on three variables, alpha, Reynolds number and Mach number, rather than six. This simplifies the number of wind tunnel tests that are needed to acquire the same information (Anderson 57-59). An example of CL vs alpha on a NACA airfoil is to the right. References 1. Anderson, John D. Fundamentals of Aerodynamics, 4th Ed. McGraw-Hill, 2007. 2. Anderson, John D. Aircraft Performance and Design, WCB/McGraw-Hill, 1999. 3. Stevens, Brian L. and Lewis, Frank L. Aircraft Control and Simulation, 2nd Ed. John Wiley & Sons, Inc, 2003.